This site says that water vapor isn't visible.
However, take a look at this picture:
Isn't that water vapor?
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Water vapour is a clear and colourless gas, so it can't be seen by the naked eye.
What you see in the photo in your second link is (partially) condensed water vapour, i.e. fog (or mist). Fog contains tiny, discrete water droplets and light bounces off their surface in random directions, causing the visibility.
Water vapour by contrast only contain free molecules, too small for light to bounce off, so pure water vapour (without any condensate) is invisible, like most gases (some gases are clear but coloured like chlorine gas).
Trouble is caused by definitions of steam and vapour in physics and in common language.
Physical definition of water vapour and steam is gaseous phase of water. In common language it is "the white cloud above pot with warm water in it when it is cold there".
Take glass kettle and put it on a stove and boil the water in it.
You will see bubbles growing in the bottom and disappearing in the water volume. Those bublles contain water vapour only. If you reach boiling temperature in whole volume, such bublles stop vanishing and will run to the top where they pop.
You will also see that those bubbles are colourless instead of being white or grey. That means they are filled with (invisible) colourless gas - water vapour.
Once they pop, the vapour leaves hot water surrounding and enter colder air where it dissolves until it reaches saturation point and no more water vapour can dissolve - so it condensates. Above the kettle it forms "steam", outside it forms fog and clouds. It condensate on any interface it can - lid, dust, water droplet - and form humid air - water droplets mixture. Both phases are colourless but because of different indices fo refraction the light is shattered in there and you can see white (grey) cloud of steam.
Observing the steam raising from the kettle you can see it vanishes. It is caused by high-temperature droplets reaching unsatureated air, evaporating again and forming one colourless phase - humid air.
The bubble forms when (small ammount of) liquid water goes gaseous, the bubble contain water only. There are no gases - there is only water vapour in it. When the bubble pops, the vapour in it will be released to the mixture of gases called air and will difuse in it (increasing absolute humidity). If it was not water but liquid chlorine, chlorine gass will diffuse instead (increasing its concentration in the air). If it was a block of dry ice, carbon dioxide gas is released and dissolves in the air.
When the temperature is below the dew point (driven by humidity and pressure) the water content in the (over)saturated air will condensate. In case of boiling water, the humidity changes (increases) and thus the water in the air condensate and form the white opaque steam cloud. In case of chlorine, you will see yellow transparent cloud. In case of dry ice the heat consumed to warming the block and evaporating the carbon dioxide causes decrease of temperature of the humid air in the surroundings. When the temperature drops below dew point, water will condensate and you will see white, opaque cloud.
The steam cloud is white because water does not absorb light of specific wavelength (colour). It is opaque because of large ammount of small particles that are round or randomly oriented. Thus they are reflecting light to random directions. Cloud made of copper sulfate, $CuSO_4\times5H_2O$, dust will be blue (because of selective light absorbtion) and opaque (because of light scattering).
Suppose we have small volume of hot water vapour only surrounded by cold humid air.
What you will observe strongly depends on tempreature(s), pressure and volumes. If the air humidity is low enough, the water will dissolve without any effects. If the humidity is large enough, the temperature in water vapour and close the border may drop below dew point and because of oversaturated state the vapour may condensate and release another heat (condensation enthalpy). This will form the visible cloud. The water droplets then diffuse in the air and may evaporate (and consume same ammount of heat as it was released during condensation) or dissipate in the volume. In both cases the cloud will become indistiguishable form the rest of the volume.
Your question is partly a language question. Natural language is terribly imprecise and ambiguous. This is the underlying reason for all sciences to develop their own terminology.
In this case two of the four meanings Merriam-Webster lists for vapor are unfortunately almost the opposites of each other.
Yes, the white clouds you see are "vapor" in everyday language, as every adult is happy to point out to a three-year-old. This is the first definition in Merriam-Webster's entry on vapor:
Diffused matter (as smoke or fog) suspended floating in the air and impairing its transparency.
This "vapor" is a fog, just like clouds: Tiny drops of fluid suspended floating in the air.
No, what you see is emphatically not "vapor" in the scientific sense. Scientifically, vapor is defined as
a substance in the gaseous state as distinguished from the liquid or solid state
as the second definition for vapor in Merriam-Webster's states. In order to know what a gas is we can look at its Wikipedia article:
A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or compound molecules made from a variety of atoms (e.g. carbon dioxide).
Water vapor, i.e. water in the gaseous state, consequently consists of individual water molecules which do not reflect or (at this scale) significantly absorb or disperse visible light due to their small size. Because the visible fog, or the clouds, above boiling water, which are called "vapor" in everyday language, consist of little droplets of fluid (not gaseous!) water, they are not "vapor" in this scientific sense. Paradoxically, water vapor in the scientific sense is exactly what you don't see in the picture.
Pretty much every gas can be condensed into a liquid at some temperature, and pretty much every liquid can be "boiled off" as a gas ※. It's just that some go through this transformation at a high temperature and others at a low temperature.
Water's transition point (at sea-level pressure) is 100 degrees C, so you mostly experience it as a liquid. Oxygen, on the other hand, boils at −183°C, so you only see the liquid when it's been condensed with special equipment.
But below its boiling point, water still evaporates into the air in relatively small amounts, until the "saturation point" is reached for a given temperature and pressure. (This is what weathermen are talking about when they talk about "percent humidity".) When water is near the saturation point (near "100 percent humidity") it switches back and forth between liquid and gas, and so tiny droplets of water can end up suspended in mid-air. It is these tiny droplets that you see in fog, clouds, the "steam" arising out of a tea kettle, etc.
※ I say "pretty much" because some materials may go through a chemical transformation of some sort before they reach their "boiling point".